Csidh Reference Implementation

To build with default parameters, simply run make and then sudo make install to install the corresponding tools to the system. The default parameter BITS is set to 512.

To build a shared library and the corresponding csidh-p*-util program, simply run:

make shared-library

To install:

sudo make install

Generate one CSIDH private and public key per user:

$ csidh-p512-util -g -s demo-512-0.secret  -p demo-512-0.public
$ csidh-p512-util -g -s demo-512-1.secret  -p demo-512-1.public

Perform a key agreement from the perspective of each respective user:

$ csidh-p512-util -d -s demo-512-0.secret  -p demo-512-1.public
c7cee77cb809e99a3d38c661f53fe1a1be0f0b6071f490e6a260f7c0b28774c548e09158d5193f118a418a800683ec51be6814d156fdb34b2b3310d3ae8f8b4a
$ csidh-p512-util -d -s demo-512-1.secret  -p demo-512-0.public
c7cee77cb809e99a3d38c661f53fe1a1be0f0b6071f490e6a260f7c0b28774c548e09158d5193f118a418a800683ec51be6814d156fdb34b2b3310d3ae8f8b4a

It is also possible to use stdin and stdout:

$ cat demo-512-0.secret | csidh-p512-util -d -p demo-512-1.public
c7cee77cb809e99a3d38c661f53fe1a1be0f0b6071f490e6a260f7c0b28774c548e09158d5193f118a418a800683ec51be6814d156fdb34b2b3310d3ae8f8b4a
$ cat demo-512-0.secret demo-512-1.public | csidh-p512-util -d
c7cee77cb809e99a3d38c661f53fe1a1be0f0b6071f490e6a260f7c0b28774c548e09158d5193f118a418a800683ec51be6814d156fdb34b2b3310d3ae8f8b4a

To build a static library and a statically linked csidh-p*-util program, simply run:

make static-library

The build may be configured with other arguments:

• BITS is one of the supported parameter sets.
• UINT_IMPL is an unsigned integer implementation.
• FP_IMPL is a finite field implementation.

For example:

make BITS=1024

builds the code with a 1024-bit parameter set, and

make UINT_IMPL=ui.c FP_IMPL=fp.c

uses generic C arithmetic instead of assembly.

Other parameter sets may be used by creating a directory modelled after the p512/ and p1024/ folders, optionally including specialized ui.s and fp.s files for assembly arithmetic. Else the generic C implementation will be used.

To build the benchmark code, run "make bench"; it also supports the arguments listed above. To configure benchmarking, use the following options:

• BENCH_ITS is the number of iterations.
• BENCH_VAL benchmarks public-key validation.
• BENCH_ACT benchmarks the group action.

For example,

make bench BENCH_ITS=1000 BENCH_ACT=1 BENCH_VAL=0

builds a benchmark for 1000 iterations of the group action without public-key validation.

Benchmarks

A simple benchmark and CSIDH shared secret agreement demonstration on use with a Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz:

$ csidh-p512-bench
doing 1000 iterations of validation and action.
iterations: 1000
clock cycles: 125700756 (125.7*10^6)
wall-clock time: 48.493 ms
stack memory usage: 4368 b

Shared secret derivation with timing information:

$ csidh-p512-demo

Alice's private key   (  0.500 ms):
  0c0c010d4dfeecd0025ecf1f2b11bed02be3422f1feddbec5dbb301e1315f02f4c0124e55f

Bob's private key     (  0.404 ms):
  ecd0b4f23b3e33d2e1345c45ee4502def2bf122114ef41b053eee04425cdb05d1d43e2e5c1

Alice's public key    ( 70.244 ms):
  3a6e03ff0cfe3fcfac6f4b4ea69fa62366a8a20051061814926b535c38fc4a015dc6f0e6bc3dc449e5a4f9117e7696470f96488e9fab164d6ce0c39d5ea6fdac

Bob's public key      ( 37.351 ms):
  54ae89e13e63dc86065f96a210598dbe81f790e4c519735bea6e703804677931462f7c50e2411a9a515f26a519159a935e4f3db96feef0543396171050fc7322

Alice's shared secret ( 36.721 ms):
  2dfee422f92e7ee93a2ecd102300d4a4b67c66fd451244fb444f5e9675c6f4dc6e1a55d81818194019b63efc9dcb67b518b344ade7476e2acf870186cd26421b

Bob's shared secret   ( 42.306 ms):
  2dfee422f92e7ee93a2ecd102300d4a4b67c66fd451244fb444f5e9675c6f4dc6e1a55d81818194019b63efc9dcb67b518b344ade7476e2acf870186cd26421b

    equal.

The same benchmark and key agreement on a Raspberry Pi 4 Model B Rev 1.1:

$ csidh-p512-bench
doing 1000 iterations of validation and action.
iterations: 1000
clock cycles: 29717321 (29.7*10^6)
wall-clock time: 549.508 ms
stack memory usage: 4768 b

Shared secret derivation with timing information:

$ csidh-p512-demo

Alice's private key   (  0.371 ms):
d5311d13ddb14c3ebf52bc4020fd5fc34cfc1fef223512df3d25343d55ed445d4fb0c115f2

Bob's private key     (  0.415 ms):
dd0eed2dfd0401eeb4454b41bf2ce3bccf1423c0232cec02bb3ff2e20bee15bdded511fb2e

Alice's public key    (571.734 ms):
50721ee9067ece5fbae5d6864017352d0b3fb892daa828cbb618baeb4288475b74a60bd5341c2893025549fb6a0288330d8eb056a69be5a6d0822245558b1b82

Bob's public key      (529.899 ms):
1b3d030d38f70ee2aa5083d3681aa4a13cd0f6469f7ac37033c4dc9c66c1fa164aff569fafda029bb48d7d2a279895ef151372f3f7c9cc236d9a6f0fd0223570

Alice's shared secret (578.907 ms):
5a075d7f4f5e37fa95bd6103bc71bdd2e98173078e26dd2aeaf3f9581ff847056e6e781cea986991e43ffeb4e68fc2763a9059088296ded0a0df415ffd4913fa

Bob's shared secret   (534.403 ms):
5a075d7f4f5e37fa95bd6103bc71bdd2e98173078e26dd2aeaf3f9581ff847056e6e781cea986991e43ffeb4e68fc2763a9059088296ded0a0df415ffd4913fa

  equal.

The same benchmark and key agreement on a Raspberry Pi 3 Model B Rev 1.2:

$ csidh-p512-bench
doing 1000 iterations of validation and action.
iterations: 1000
clock cycles: 22086467 (22.1*10^6)
wall-clock time: 1148.395 ms
stack memory usage: 4768 b

Shared secret derivation with timing information:

$ csidh-p512-demo

Alice's private key   (  0.301 ms):
  4d004fb0fe1be55c050c03b03f31d30f0d2b245bd2e21103fe40b4f520345cc5b554e5ecde

Bob's private key     (  0.240 ms):
  0d3f0ccb504c2debe14c51b21db4c0f22dccf5e2ee5cbbe1ed20f322c414f2d23440d00223

Alice's public key    (1175.329 ms):
  4f6c8630d59f524651d0caa010605528df9e8588a6560b94bde3ab276745ebb164ec65d9c6f7ac04d8787d7084118ce48d36eba3f4d8afcf25bdee60a5dbcf49

Bob's public key      (1063.863 ms):
  621279da5aab0140668e4db8d0ad021e92fdb7119a7950a69cd98337bd31366d5385238f75f58fc0a28efc71e5b0a0f798a474c91048843253e05acf33cfdc8e

Alice's shared secret (1158.707 ms):
  1eb8091dbc7e3949a22f159676506a5de136ca3912624b0a1fb2d24dce5a5b65bb3724d66834c166125f0192aa5260b338ae156e28251d9309a67d297c722684

Bob's shared secret   (1077.129 ms):
  1eb8091dbc7e3949a22f159676506a5de136ca3912624b0a1fb2d24dce5a5b65bb3724d66834c166125f0192aa5260b338ae156e28251d9309a67d297c722684

    equal.

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